Of course, if you're not going to use backreferencing ($1, $2, etc) with those parens, you'll probably want to turn off the backreferencing with ?: inside the parens; no need to create backreferences if you're not going to use 'em: 
foreach (qw(AAXXBB AAYBB AAXYBB AAYBB AYBB)) {
   printf("%-7s", $_);
   print (($_ =~ /^AA(XX|Y)BB$/) ? "yes  " : "no   ");
   print (($_ =~ /^AAXX|YBB$/)   ? "yes  " : "no   ");
   print "\n";
}
$ perl j.pl
AAXXBB yes  yes
AAYBB  yes  yes
AAXYBB no   yes
AAYBB  yes  yes
AYBB   no   yes
$ cat x.pl
foreach (qw(AAXXBB AAYBB AAXYBB AAYBB AYBB)) 
{
   printf("%-7s", $_);
   print (($_ =~ /^AA(?:XX|Y)BB$/) ? "yes  " : "no   ");
   print (($_ =~ /^AAXX|YBB$/)   ? "yes  " : "no   ");
   print "\n";
} 
AAXXBB yes  yes
AAYBB  yes  yes
AAXYBB no   yes
AAYBB  yes  yes
AYBB   no   yes
-- b